A154413 a(n) = A006551(n) - A018224(n).

0, 0, 0, 2, 30, 202, 2016, 14394, 151290, 1294478, 15660744, 162298842, 2274318228, 27968231436, 447527038848, 6382757516250, 114890215021650, 1865385066804550, 37307710791708600, 679562209260462054

Offset: 0

Author

Roger L. Bagula, Jan 09 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A006551, A018224.

Programs

Mathematica

t[n_, k_] = Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}];
a0 = Table[t[n, Floor[n/2]], {n, 1, 30}];
b0 = Table[Binomial[n, Floor[(n)/2]]^2, {n, 0, 29}];
a=a0-b0

Formula

a(n) = Eulerian[n,Floor[n/2]] - Binomial[n,Floor[n/2]]^2.